a theoretical introduction to numerical analysis

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A Theoretical Introduction To Numerical Analysis

Author : Victor S. Ryaben'kii
ISBN : 1584886072
Genre : Mathematics
File Size : 74. 67 MB
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A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.

Introduction To Numerical Analysis

Author : Arnold Neumaier
ISBN : 0521336104
Genre : Mathematics
File Size : 56. 59 MB
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This 2001 textbook provides an introduction to constructive methods that provide accurate approximations to the solution of numerical problems using MATLAB.

An Introduction To Numerical Analysis

Author : Endre Süli
ISBN : 0521007941
Genre : Mathematics
File Size : 49. 52 MB
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Introduction to numerical analysis combining rigour with practical applications. Numerous exercises plus solutions.

Introduction To Numerical Analysis Using Matlab

Author : Rizwan Butt
ISBN : 076377376X
Genre : Mathematics
File Size : 65. 41 MB
Format : PDF
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Part of the new Digital Filmmaker Series! Digital Filmmaking: An Introductionis the first book in the newDigital Filmmaker Series. Designed for an introductory level course in digital filmmaking, it is intended for anyone who has an interest in telling stories with pictures and sound and won't assume any familiarity with equipment or concepts on the part of the student. In addition to the basics of shooting and editing, different story forms are introduced from documentary and live events through fictional narratives. Each of the topics is covered in enough depth to allow anyone with a camera and a computer to begin creating visual projects of quality.

Introduction To Numerical Analysis

Author : Josef Stoer
ISBN : 9781475755923
Genre : Mathematics
File Size : 76. 67 MB
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This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Introduction To Numerical Methods In Differential Equations

Author : Mark H. Holmes
ISBN : 9780387681214
Genre : Mathematics
File Size : 26. 2 MB
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This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

An Introduction To Numerical Methods And Analysis

Author : James F. Epperson
ISBN : 9781118626238
Genre : Mathematics
File Size : 63. 22 MB
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Introduction To Numerical Analysis

Author : Devi Prasad
ISBN : 1842652117
Genre : Mathematics
File Size : 45. 26 MB
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An Introduction to Numerical Analysis is designed for a first course on numerical analysis for students of Science and Engineering including Computer Science. The text contains derivation of algorithms for solving engineering and science problems and also deals with error analysis. It has numerical examples suitable for solving through computers. The special features are comparative efficiency and accuracy of various algorithms due to finite digit arithmetic used by the computers.

Theory And Applications Of Numerical Analysis

Author : G. M. Phillips
ISBN : 0080519121
Genre : Mathematics
File Size : 84. 95 MB
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Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. a unique blend of theory and applications two brand new chapters on eigenvalues and splines inclusion of formal algorithms numerous fully worked examples a large number of problems, many with solutions

A Graduate Introduction To Numerical Methods

Author : Robert Corless
ISBN : 9781461484530
Genre : Mathematics
File Size : 27. 81 MB
Format : PDF, ePub
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This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

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